All PSAT Math Resources
Example Questions
Example Question #562 : Arithmetic
Which of the following is a graph for the values of defined by the inequality stated above?
Begin by solving for :
Now, this is represented by drawing an open circle at 6 and graphing upward to infinity:
Example Question #1 : How To Find Value With A Number Line
If the tick marks are equally spaced on the number line above, what is the average (arithmetic mean) of x, y, and z?
7
4
5
6
8
6
First, we must find out by how much they are spaced by. It cannot be 1, since 4(4) = 16, which is too great of a step in the positive direction and exceeds the equal-spacing limit. 2 works perfectly, however, as 4(2) equals 8 and fits in line with the equal spacing.
Next, we can find the values of x and y since we are given a value of 6 for the third tick mark. As such, x (6 – 4) and y (6 – 2) are 2 and 4, respectively.
Finally, z is 4 steps away from y, and since each step has a value of 2, 2(4) = 8, plus the value that y is already at, 8 + 4 = 12 (or can simply count).
Finding the average of all 3 values, we get (2 + 4 + 12)/3 = 18/3 = 6.
Example Question #11 : Number Lines And Absolute Value
How many numbers 1 to 250 inclusive are cubes of integers?
The cubes of integers from 1 to 250 are 1, 8, 27,64,125,216.
Example Question #3 : How To Find Value With A Number Line
Refer to the above number line. Which of the points is most likely the location of the number ?
, so
Therefore,
On the number line, appears between 0.3 and 0.4 and is the correct choice.
Example Question #1 : How To Add Negative Numbers
How many elements of the set are less than ?
One
Four
Three
None
Two
Four
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set are less than this positive number.
Example Question #1781 : Psat Mathematics
a, b, c are integers.
abc < 0
ab > 0
bc > 0
Which of the following must be true?
a + b < 0
a > 0
b > 0
a – b > 0
ac < 0
a + b < 0
Let's reductively consider what this data tells us.
Consider each group (a,b,c) as a group of signs.
From abc < 0, we know that the following are possible:
(–, +, +), (+, –, +), (+, +, –), (–, –, –)
From ab > 0, we know that we must eliminate (–, +, +) and (+, –, +)
From bc > 0, we know that we must eliminate (+, +, –)
Therefore, any of our answers must hold for (–, –, –)
This eliminates immediately a > 0, b > 0
Likewise, it eliminates a – b > 0 because we do not know the relative sizes of a and b. This could therefore be positive or negative.
Finally, ac is a product of negatives and is therefore positive. Hence ac < 0 does not hold.
We are left with a + b < 0, which is true, for two negatives added must be negative.
Example Question #11 : Negative Numbers
What is ?
45
A negative number divided by a negative number always results in a positive number. divided by equals . Since the answer is positive, the answer cannot be or any other negative number.
Example Question #1 : Negative Numbers
Solve for :
Begin by isolating your variable.
Subtract from both sides:
, or
Next, subtract from both sides:
, or
Then, divide both sides by :
Recall that division of a negative by a negative gives you a positive, therefore:
or
Example Question #1 : Negative Numbers
If is a positive number, and is also a positive number, what is a possible value for ?
Because is positive, must be negative since the product of two negative numbers is positive.
Because is also positive, must also be negative in order to produce a prositive product.
To check you answer, you can try plugging in any negative number for .
Example Question #1 : Negative Numbers
, , and are all negative odd integers. Which of the following three expressions must be positive?
I)
II)
III)
II only
I only
None of these
All of these
III only
All of these
A negative integer raised to an integer power is positive if and only if the absolute value of the exponent is even. Since the sum or difference of two odd integers is always an even integer, this is the case in all three expressions. The correct response is all of these.
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